1. Field of the Invention
This invention relates to the measurement of volumetric fluid flow in a closed medium and more specifically to the measurement of volumetric fluid flow when the flow is unsteady or pulsating.
2. Description of Prior Art
Many industries, such as natural gas and oil industries, rely on pipelines to transport their products from location to location. During this transfer, the measurement of the oil or gas transferred is required. In the past, these industries have relied upon calibrated orifice differential pressure measurements as a standard method of indicating the volumetric fluid flow of their products in these pipelines. The principal reasons for the near universal usage of this orifice measurement technique are its simplicity and excellent repeatability under steady fluid flow conditions. Since an orifice differential pressure meter is an inferential one, errors can result when flow conditions deviate from the steady state flow conditions or from the conditions from which constants used to calibrate the meter were derived.
For example, the general equation for an orifice measurement is Q=K(.DELTA.P).sup.1/2 where K is a proportionality factor or constant, .DELTA.P is the orifice differential pressure, and Q is the resulting volumetric flow rate. This equation illustrates the basic nonlinear nature of the orifice technique. It is because of this nonlinearity that the so-called square root error exists when the flow inside the pipe or closed medium is pulsating or varying substantially from a steady state or steady flow condition. Simply stated, the orifice average differential pressure is higher when fluid flow is pulsating than it would be with a smooth steady state flow, i.e., when the net total flow is the same over a time interval. This would be true even though the orifice constant factor K is not affected by pulsations. If the flow or Q is inferred from an average .DELTA.P, then the flow measurement would be incorrect in the presence of unsteady flow conditions or pulsations. Note, however, that if the continuous square root of the instantaneous .DELTA.P was taken, and the resultant values averaged, then the square root error would vanish. The flow inferred then would be correct unless the pulsations somehow altered the calibration coefficient K for the orifice.
Most pressure indicators and recorders used by the industry in orifice meter applications do not have sufficient frequency response to track the flow pulsations normally produced by compressor stations, "hunting" regulators or vortex shedding conditions in the piping system. They tend to average .DELTA.P although they may give some indications of pulsations on the recording chart (commonly referred to as "paint"). When these charts are read, there is a tendency to ignore the "paint" caused by pressure pulsations and more of a tendency to average the .DELTA.P pressure. The result of any analysis process which averages .DELTA.P before its square root is extracted will therefore produce what is termed "the square root error".